Those donkeys deserve some respect, despite any recent injury. I believe the correct question is: "How many ~8.7 day increments in a year can be devoid of all but one holiday?" As you might suspect... the answer has already been derived.

Sometimes I feel like there is a computer that randomly puts a few words together, put a random day of the year, then tell everyone what to do for a day. I take all these "_____ _____ day" as a joke now. Along withe "___-____month" as a joke.
I'm going to make Jan 31 Tell a secret day.